Game Theory “How to Win the Game!”

Definition: Game theory is the mathematics of strategy.

Two Types of Games Games of Chance Total Information Games A game whose outcome is strongly influenced by some randomizing device, such as dice, spinners or cards. Total Information Games A game where the players know, in advance, all the game options and a player’s decisions throughout the game are based on the previous player’s decision.

A Winning Strategy: Analyze a Total Information Game to determine the strategy that gives you the best chance to win the game.

A list of all the things that could happen in a situation. (game) Possible Outcomes: A list of all the things that could happen in a situation. (game)

Lesson Objectives: Gather data to determine winning outcomes for a game. Analyze the data to determine the best winning strategy. List all the possible outcomes for a game. Analyze the possible outcomes to determine the best winning strategy. Apply this winning strategy to similar games.

Experimental Probability: Experimental probability is the ratio of the number of desirable occurrences of an event to the total number occurrences of the event. Example: Tossing a coin If you tossed a coin 10 times, recorded heads 7 times and tails 3 times, then the experimental probabilities are: P(H) = 7/10 P(T) = 3/10 70% 30%

Theoretical Probability: Theoretical probability is the ratio of the number of ways the event can occur to the total number of possibilities in the sample space. Example: tossing a die P(1)=1/6 P(2)=1/6 P(3)=1/6 P(2)=1/6 P(5)=1/6 P(6)=1/6

In a nutshell: Experimental Probability is what happened when you did the activity. Theoretical Probability is what should have happened if everything turned out the way is was supposed to.

Time to move on to the lesson.